Pat the veal shanks dry with paper towels. Season both sides with salt and pepper, then dust lightly with flour and shake off any excess.

Tie kitchen twine around the circumference of each shank to keep the meat in place during braising.

Heat the olive oil and butter in a Dutch oven over medium-high heat until the butter foam subsides and the fat shimmers.

Add two shanks in a single layer and sear for 4 minutes without moving them, until deeply browned on the underside. Flip and sear the other side for 3 minutes. Transfer to a plate and repeat with the remaining shanks.

Reduce the heat to medium. Add the onion, celery, and carrot to the same pot. Cook, stirring occasionally, for 8 to 10 minutes until the vegetables are soft and pale gold.

Add the garlic and cook for 1 minute until fragrant.

Pour in the white wine, scraping the browned bits from the bottom of the pot with a wooden spoon. Let the wine bubble and reduce by half, about 4 minutes.

Add the warm broth, crushed tomatoes (if using), bay leaves, and thyme. Stir to combine.

Nestle the seared shanks back into the pot in a single layer. The liquid should come about halfway up the sides of the shanks. Add more broth if needed.

Bring to a gentle simmer, then reduce heat to low. Cover with the lid slightly ajar and braise for 1 hour 45 minutes to 2 hours, turning the shanks once halfway through, until the meat is very tender and pulls away from the bone easily.

In the last 20 minutes, remove the lid fully to allow the sauce to reduce to a light coating consistency.

Combine the chopped parsley, lemon zest, and minced garlic in a small bowl. Mix well.

Remove the bay leaves and thyme sprig. Taste the sauce and adjust salt if needed.

Remove the kitchen twine from the shanks. Let the pot rest off the heat, covered, for 10 minutes.

Plate each shank over risotto alla Milanese or soft polenta. Spoon braising sauce over the top and finish each portion with a generous pinch of gremolata.